## Research Interests

My research interests primarily focus on Linear Algebra and Dynamical Systems.

In Linear Algebra, I am mainly interested in spectral properties of matrix valued functions. Most of my work is devoted to the study of degeneracies (coalescence of eigenvalues or singular values, loss of rank) for matrices that depend on parameters, and of their effect on the associated subspaces. Numerical tools developed in my works include algorithms for smoothly computing eigendecomposition, SVD and Berry phase for matrix functions of one parameter and for detecting degeneracies (e.g., conical intersections and points of loss of rank) for matrix functions of two or more parameters.

In Dynamical Systems, I have worked on numerical continuation of, and detection of bifurcations on, multi-dimensional manifolds of equilibria for ordinary and partial differential equations, as well as on issues related to finite-time blow-up and extinction of solutions and synchronization in networks.

## Recent/selected papers (published, accepted, or preprints)

Stabilization of synchronous tridiagonal network motion

L Dieci, C Elia, A Pugliese

arXiv:2408.01066, 2024

Cusp bifurcations: numerical detection via two-parameter continuation and computer-assisted proofs of existence

JP Lessard, A Pugliese

arXiv:2404.00535, 2024

SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters

L Dieci, A Pugliese

Linear Algebra and its Applications, 2024, DOI: 10.1016/j.laa.2024.07.021

Takagi factorization of matrices depending on parameters and locating degeneracies of singular values

L Dieci, A Papini, A Pugliese

SIAM Journal on Matrix Analysis and Applications, 2022, DOI: 10.1137/21m1456273

Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters

L Dieci, A Papini, A Pugliese

Numerical Algorithms, 2022, DOI: 10.1007/s11075-022-01326-7

A note on the Kuramoto-Sivashinsky equation with discontinuity

L D'Ambrosio, M Gallo, A Pugliese

Mathematics in Engineering, 2021, DOI: 10.3934/mine.2021041

Coalescing points for eigenvalues of banded matrices depending on parameters with application to banded random matrix functions

L Dieci, A Papini, A Pugliese

Numerical Algorithms, 2019, DOI: 10.1007/s11075-018-0525-z

Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems

A Colombo, N Del Buono, L Lopez, A Pugliese

Discrete and Continuous Dynamical Systems - series B, 2018, DOI: 10.3934/DCDSB.2018166

Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions

M Gameiro, JP Lessard, A Pugliese

Foundations of Computational Mathematics, 2016, DOI: 10.1007/s10208-015-9259-7

Blow-up profile for solutions of a fourth order nonlinear equation

L D'Ambrosio, JP Lessard, A Pugliese

Nonlinear Analysis: Theory, Methods & Applications, 2015, DOI: 10.1016/J.NA.2014.12.026

Hermitian matrices of three parameters: perturbing coalescing eigenvalues and a numerical method

L Dieci, A Pugliese

Mathematics of Computation, 2015, DOI: 10.1090/mcom/2977

Approximating Coalescing Points for Eigenvalues of Hermitian Matrices of Three Parameters

L Dieci, A Papini, A Pugliese

SIAM Journal on Matrix Analysis and Applications, 2013, DOI: 10.1137/120898036

Hermitian matrices depending on three parameters: Coalescing eigenvalues

L Dieci, A Pugliese

Linear Algebra and its Applications, 2012, DOI: 10.1016/J.LAA.2012.01.009

Locating coalescing singular values of large two-parameter matrices

L Dieci, MG Gasparo, A Papini, A Pugliese

Mathematics and Computers in Simulation, 2011, DOI: 10.1016/j.matcom.2010.10.005

Two-Parameter SVD: Coalescing Singular Values and Periodicity

L Dieci, A Pugliese

SIAM Journal on Matrix Analysis and Applications, 2009, DOI: 10.1137/07067982X

Singular values of two-parameter matrices: an algorithm to accurately find their intersections

L Dieci, A Pugliese

Mathematics and Computers in Simulation, 2008, DOI: 10.1016/j.matcom.2008.03.012